Kumar took first place in the vote, bringing in nearly 55 percent of the 559 votes, while Lapidus came in second with 29 percent of the votes, as reported by the Dane County Clerk's Office as of press time.
UW sophomore Adam Korn, who received 12 percent of the vote, and UW freshman Sean Cornelius, with nearly 5 percent of the vote, will not advance to the general election.
After the ballots were counted, Kumar enjoyed a victory party at Hawk's Bar and Grill with colleagues and friends.
"I'm ecstatic," Kumar said. "I'm so happy that I have an amazing group of hard working volunteers and an amazing campaign team."
Although Lapidus said he is disappointed that all four candidates could not advance, he said is also excited for the upcoming general election.
"I think we both have a really decent shot at both of us increasing our vote totals in the general election," Kumar said.
Among the issues addressed in his campaign, Kumar said he will focus on tenants' rights, alternatives for incarceration and keeping "big bucks" retailers out of the county.
Kumar has already garnered support from Korn, who said Tuesday he will endorse Kumar's campaign for the upcoming general election.
"Ashok is much better at asking people to help him, and I think he's going to do great," Korn said. "Whatever he needs me to do, I'll do for him."
Lapidus, who claimed some of his opponents chose to "attack" him and his more conservative values, said he hopes the election will continue with a "dialogue about the issues" not "just party politics."
Despite leaving the campaign trail behind, Korn and Cornelius said they were happy just to experience the election process.
"I learned that I'm not a candidate, I'm going to be the guy behind the guy," Korn said. "I'm going to enjoy the college life again and not have to wear a button and [campaign] T-shirt the whole time."
Cornelius, who had the least money to campaign, said the election results reflected his expectations for the race.
"Regardless of the outcome, I'm happy with the race I ran; it was a lot of fun," he said.
Cornelius added Kumar and Lapidus have a healthy knowledge of politics and activism in government and either one will "make a fine county supervisor."
"And at the end of this, we'll have a student representative sitting on the Board," he said.
Voter turnout was low given the total number of district residents, but students will get another chance to voice their opinion in April.
Each victorious candidate had a different opinion on the turnout, as Kumar was happy to see students show up, but Lapidus felt more could have voted.
"We probably have a couple more hundred supporters but some of them didn't turn out," Lapidus said. "So I'm disappointed with the voter turnout in general."
Kumar attributed the lack of student turnout to the recent weather troubles that have hit Madison and praised those that did vote.
"To the ones that voted, it's a testament to the fact that Madison students are very progressive and stand for progressive issues," he said.